Bessel Functions - 10.41 Asymptotic Expansions for Large Order

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
10.41.E8 p = ( 1 + z 2 ) - 1 2 𝑝 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle p=(1+z^{2})^{-\frac{1}{2}}}}
p = (1+z^{2})^{-\frac{1}{2}}		 

p = (1 + (z)^(2))^(-(1)/(2))
 
p == (1 + (z)^(2))^(-Divide[1,2])
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10.41#Ex3 U 1 ⁒ ( p ) = 1 24 ⁒ ( 3 ⁒ p - 5 ⁒ p 3 ) subscript π‘ˆ 1 𝑝 1 24 3 𝑝 5 superscript 𝑝 3 {\displaystyle{\displaystyle U_{1}(p)=\tfrac{1}{24}(3p-5p^{3})}}
U_{1}(p) = \tfrac{1}{24}(3p-5p^{3})		 

U[1](p) = (1)/(24)*(3*p - 5*(p)^(3))
 
Subscript[U, 1][p] == Divide[1,24]*(3*p - 5*(p)^(3))
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10.41#Ex4 U 2 ⁒ ( p ) = 1 1152 ⁒ ( 81 ⁒ p 2 - 462 ⁒ p 4 + 385 ⁒ p 6 ) subscript π‘ˆ 2 𝑝 1 1152 81 superscript 𝑝 2 462 superscript 𝑝 4 385 superscript 𝑝 6 {\displaystyle{\displaystyle U_{2}(p)=\tfrac{1}{1152}(81p^{2}-462p^{4}+385p^{6% })}}
U_{2}(p) = \tfrac{1}{1152}(81p^{2}-462p^{4}+385p^{6})		 

U[2](p) = (1)/(1152)*(81*(p)^(2)- 462*(p)^(4)+ 385*(p)^(6))
 
Subscript[U, 2][p] == Divide[1,1152]*(81*(p)^(2)- 462*(p)^(4)+ 385*(p)^(6))
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10.41#Ex5 U 3 ⁒ ( p ) = 1 4 14720 ⁒ ( 30375 ⁒ p 3 - 3 69603 ⁒ p 5 + 7 65765 ⁒ p 7 - 4 25425 ⁒ p 9 ) subscript π‘ˆ 3 𝑝 1 4 14720 30375 superscript 𝑝 3 3 69603 superscript 𝑝 5 7 65765 superscript 𝑝 7 4 25425 superscript 𝑝 9 {\displaystyle{\displaystyle U_{3}(p)=\tfrac{1}{4\;14720}\*(30375p^{3}-3\;6960% 3p^{5}+7\;65765p^{7}-4\;25425p^{9})}}
U_{3}(p) = \tfrac{1}{4\;14720}\*(30375p^{3}-3\;69603p^{5}+7\;65765p^{7}-4\;25425p^{9})		 

U[3](p) = (1)/(414720)*(30375*(p)^(3)- 369603*(p)^(5)+ 765765*(p)^(7)- 425425*(p)^(9))
 
Subscript[U, 3][p] == Divide[1,414720]*(30375*(p)^(3)- 369603*(p)^(5)+ 765765*(p)^(7)- 425425*(p)^(9))
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10.41#Ex6 V 1 ⁒ ( p ) = 1 24 ⁒ ( - 9 ⁒ p + 7 ⁒ p 3 ) subscript 𝑉 1 𝑝 1 24 9 𝑝 7 superscript 𝑝 3 {\displaystyle{\displaystyle V_{1}(p)=\tfrac{1}{24}(-9p+7p^{3})}}
V_{1}(p) = \tfrac{1}{24}(-9p+7p^{3})		 

V[1](p) = (1)/(24)*(- 9*p + 7*(p)^(3))
 
Subscript[V, 1][p] == Divide[1,24]*(- 9*p + 7*(p)^(3))
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10.41#Ex7 V 2 ⁒ ( p ) = 1 1152 ⁒ ( - 135 ⁒ p 2 + 594 ⁒ p 4 - 455 ⁒ p 6 ) subscript 𝑉 2 𝑝 1 1152 135 superscript 𝑝 2 594 superscript 𝑝 4 455 superscript 𝑝 6 {\displaystyle{\displaystyle V_{2}(p)=\tfrac{1}{1152}(-135p^{2}+594p^{4}-455p^% {6})}}
V_{2}(p) = \tfrac{1}{1152}(-135p^{2}+594p^{4}-455p^{6})		 

V[2](p) = (1)/(1152)*(- 135*(p)^(2)+ 594*(p)^(4)- 455*(p)^(6))
 
Subscript[V, 2][p] == Divide[1,1152]*(- 135*(p)^(2)+ 594*(p)^(4)- 455*(p)^(6))
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10.41#Ex8 V 3 ⁒ ( p ) = 1 4 14720 ⁒ ( - 42525 ⁒ p 3 + 4 51737 ⁒ p 5 - 8 83575 ⁒ p 7 + 4 75475 ⁒ p 9 ) subscript 𝑉 3 𝑝 1 4 14720 42525 superscript 𝑝 3 4 51737 superscript 𝑝 5 8 83575 superscript 𝑝 7 4 75475 superscript 𝑝 9 {\displaystyle{\displaystyle V_{3}(p)=\tfrac{1}{4\;14720}\*(-42525p^{3}+4\;517% 37p^{5}-8\;83575p^{7}+4\;75475p^{9})}}
V_{3}(p) = \tfrac{1}{4\;14720}\*(-42525p^{3}+4\;51737p^{5}-8\;83575p^{7}+4\;75475p^{9})		 

V[3](p) = (1)/(414720)*(- 42525*(p)^(3)+ 451737*(p)^(5)- 883575*(p)^(7)+ 475475*(p)^(9))
 
Subscript[V, 3][p] == Divide[1,414720]*(- 42525*(p)^(3)+ 451737*(p)^(5)- 883575*(p)^(7)+ 475475*(p)^(9))
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